4 Does Women’s Labor Force Participation Reduce Domestic Violence?
4.5 Endogeneity Issues
A k y c c r h s r r ss s h p al d y b w w m ’s w rk s a us and domestic violence. Endogeneity can have several sources, two of which may be present in this model, namely simultaneous causality and omitted variables. The presence of violence may lead a woman to increase or decrease her willingness to work. Most studies suggest that v l c r duc s w m ’s mpl ym du m al a d phys cal health consequences (Staggs
& Riger, 2005; Tolman & Wang, 2005), increasing tardiness and absenteeism (Lloyd, 1997;
Riger, Ahrens & Blickenstaff, 2000). On the other hand, women who are suffering from abuse might be more likely than non-abused women to seek paid work (Narayan et al., 2000). Studies from developing countries find mixed results as regards the probability that an abused woman works outside the home, since abused women are both more likely and less likely to work (Morrison & Orlando, 1999). In this case, causality would run both ways, leading to a biased coefficient on women’s mpl ym .
Work status and domestic violence are driven by a third unobserved factor, traditionalism.
These two possibilities of endogeneity suggest that in equation (1) the observed relationship b w w m ’s w rk s a us a d d m s c v l c may be biased or even spurious.
However, the direction of bias can be ambiguous. Although employment status and traditionalism is likely to be negatively correlated, the effect of traditionalism on violence could be positive or negative. Under the assumption that the incidence of violence is positively correlated with the degree of traditionalism (assuming that a more traditionally socialized spouse does not allow his wife to work), we may have a downward bias, finding a spurious negative correlation. Of course, if traditional husbands beat their wives less (and ensure that
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they work less), there could be a spurious positive correlation, leading to an overestimate of the coefficient on the employment status.66 I h s cas , h c ff c f w m ’s mpl ym status is underestimated. With respect to reverse causality, the bias is hard to quantify. If violence causes women to work less, it may lead to a downward bias of the coefficient (an underestimation); if it causes women to work more, it would lead to an upward bias. Existing l ra ur su s s ha s ma s f h ff c f w m ’s mpl ym ar m r l k ly o be underestimated (Farmer & Tiefenthaler, 2004; Johnson, 1995).
To tackle the issue of endogeneity through omitted variables and reverse causality, a two-stage linear probability model is implemented. Specifically, the first stage is defined by
Working status= Π0 + Π1z1 + Π2 z2 + υi
(2)
where working status is predicted by the exogenous instruments z1 and the control variables z2(which overlap with the variables in (1)). The error term υi captures the remaining variance of working status, which is not explained by the covariates (including the instrument) in equation (2). In the second stage, the outcome, domestic violence, is regressed on the predicted value of the endogenous variable, working status, from the first stage along with other exogenous variables. Several studies have shown ha s ma a l ar pr bab l y m d l v a “ w -stage l as squar s” pr v d s a d s ma f h av ra ff c , mak h ma ud f h coefficients easier to obtain (Miguel et al., 2004; Wooldridge, 2002; Angrist & Pischke, 2009).67 As there are questions regarding the consistency of these IV estimation techniques when there is a limited dependent variable in both stages, we also estimate the model using the two-stage residual inclusion method (2SRI) as a further robustness check.68 As wife’s working status is a binary endogenous regressor, this method delivers consistent estimates in nonlinear models (Wooldridge, 2002). In the first stage, the auxiliary equation (2) is estimated as a probit model.
66For example, one may argue that in these traditional families, gender roles are clearly delineated with ach “k w h r plac ,” l ad l ss c fl c a d v l c . Th s abs c f violence would not mean that there is no inequality, but could be a result of both partners accepting the unequal family situation.
67 Angrist and Pischke (2009) show that linear probability models (LPM) are a good option for different kinds of limited dependent variables.
68 This method was first suggested by Jerry Hausman (1987). Consistent 2SRI methods for nonlinear models have been developed by Richard W. Blundell and Richard J. Smith (1989) or Whitney K. Newey (1987).
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In the second stage regression, the endogenous variable wife’s working status is not replaced.
Instead, the residual term (υi) of equation (2) is included as an additional regressor in equation (1), which is estimated by a probit model as follows:
DV= β0 + β1 woman’s working status + β2 Characteristics Husband/Wife + β3 HH- Characteristics+ β4 Region+ γ 1+ ϵi
(3 )
Testing the coefficient γ of 1 in equation (3) evaluates whether working status is indeed endogenous.69 A key issue in this estimation is the validity of the instruments. A valid instrument should fulfill two conditions: First, it should be strongly correlated with the endogenous variable. Second, it should be exogenous in the basic model. In the current case, there are a few potentially strong candidates that could serve as good instruments, for instance type and size of the family or currently pregnant. These variables are already used in other studies to instrument w m ’s w rk s a us (Bhattacharya et al. 2011; Chin, 2007). However, the results of appropriate tests indicate that in this case only the variable cluster average of working status constitutes a valid instrument. The variable is constructed in such a way that we always use the cluster average excluding the woman being considered in each observation to avoid an in-built correlation. The cluster average of working status has a strong mpac w m ’s w mpl ym s a us, bu sh uld b d r c ly c rr la d w h husba d’s v l b hav r, h r than through its impact on women's own employment. Hence, the conditions necessary to be a valid instrument should be fulfilled in this case.
In the empirical analysis several specifications are estimated and the validity and strength of the instruments are tested.
69The coefficient of υ 1 is significant at the 5 percent level and thus, the null hypothesis of exogeneity of working status in equation (1) can be rejected. Therefore, using standard LPM regression models is not appropriate.